Mathematics Standard • Year 11 • Networks • Lesson 2
Degree Sequences · Build
Calculate degrees and convert between edge lists, neighbour lists and adjacency matrices.
Practice
Unless a question says otherwise, treat each network as a simple undirected graph: edges are unordered vertex pairs, with no loops or duplicate edges. Show your reasoning in the answer space; an edge list is enough.
Q1 · Degree sequence. For V={A,B,C,D,E} and E={AB,AC,AD,BC,DE}, write each degree and the descending degree sequence. 3 marks
Q2 · Handshake check. Add the degrees above and check against twice the edge count. 2 marks
Q3 · Neighbour list. Write the neighbours of each vertex for the same graph. 2 marks
Q1 · Degree sequence
A=3, B=2, C=2, D=2, E=1; sequence (3,2,2,2,1).
Q2 · Handshake check
3+2+2+2+1=10; 2×5=10.
Q3 · Neighbour list
A:{B,C,D}; B:{A,C}; C:{A,B}; D:{A,E}; E:{D}.